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Existence of periodic waves and kink waves in a perturbed defocusing mKdV equation
Hong Li,Hongquan Sun,Mei Liu
Keywords:Defocusing mKdV equation; Traveling wave; Abelian integral; Chebyshev system.
      In this paper, we consider the existence of periodic and kink wave solutions of a perturbed defocusing mKdV equation. Based on geometric singular perturbation theory, Chebyshev criteria and bifurcation theory of dynamic system, the wave speed conditions for the existence of periodic solutions and kink solutions are given. There is no coexistence of periodic solutions and kink solutions. The proof process does not need any explicit expression of the original defocusing mKdV periodic wave or kink wave solutions.